The ratio of the number of ducks in Farm K to the number of ducks in Farm L was 5 : 7. There were 42 fewer ducks in Farm K than in Farm L. When 12 ducks escaped from Farm L, the farmer in Farm L bought another 18 ducks. What was the new ratio of the number of ducks in Farm K to the number of ducks in Farm L in the end? Give your answer in the simplest form.
| |
Farm K |
Farm L |
| Before |
5 u |
7 u |
| Change 1 |
|
- 12 |
| Change 2 |
|
+ 18 |
| After |
5 u |
7 u + 6 |
Number of fewer ducks in Farm K than Farm L
= 7 u - 5 u
= 2 u
2 u = 42
1 u = 42 ÷ 2 = 21
Number of ducks in Farm K
= 5 u
= 21 x 5
= 105
Number of ducks in Farm L
= 7 u
= 21 x 7
= 147
New number of ducks in Farm L
= 7 u + 6
= 147 + 6
= 153
Farm K : Farm L
105 : 153
(÷ 3)35 : 51
Answer(s): 35 : 51
